Recent polls put the bombastic billionaire second behind Jeb Bush in the Republican presidential field and his harsh words on immigration have drawn widespread media attention and criticism from his political opponents.

Now Mr Trump is pointing to the death of Kathryn Steinle, a 32-year-old woman shot dead in San Francisco last week, as proof that he was right all along.

What about the undocumented immigrant with a record who killed the beautiful young women (in front of her father) in San Fran. Get smart!

Ms Steinle was walking on San Francisco's Pier 14 with her father when she was allegedly gunned down at random by Francisco Sanchez, an illegal immigrant who had been already been deported to Mexico five times.

Sanchez, who had a long criminal history, was due to be deported a sixth time but the liberal city of San Francisco is a so-called "sanctuary city", meaning its police will not hand over illegal immigrants to the US government on immigration law violations.

Francisco Sanchez has been arrested in connection with the death of Kathryn Steinle (Reuters)

Sanchez was arrested near the scene of the killing but said in a prison interview that he found the gun and shot Ms Steinle by accident.

Mr Trump called the shooting "a senseless and totally preventable act of violence committed by an illegal immigrant" and said it showed the need for a wall to be built along the 2,000 mile US-Mexican border.

"This is an absolutely disgraceful situation and I am the only one that can fix it," Mr Trump said in a statement. "Nobody else has the guts to even talk about it. That won’t happen if I become President. The American people deserve a wall to protect our jobs, economy and our safety."

Most of the other 15 Republicans running for president initially tried to ignore Mr Trump but two recent polls show him at the front of the pack and second only to Jeb Bush.

Mr Bush, who is married to a Mexican-American, said Mr Trump's comments were "extraordinarily ugly" and said he was personally offended by the businessman's language.

"He’s doing this to inflame and incite and to draw attention, which seems to be the organising principle of his campaign,” Mr Bush told the New York Times.

Leading Republicans fear that Mr Trump's freewheeling campaign will only further damage the party's relationship with Hispanic voters, an increasingly important voting bloc in American elections.

Barack Obama won 71 per cent of the Hispanic vote in 2012 and Republicans know they will have to improve their standing with America's fastest growing demographic group if they hope to take back the White House next year.